I recently googled "David Jackson Burnette" after having a discussion of descendents at a recent Thanksgiving meal. I read your post and was just wondering if we were speaking of the same person. Your post says that Joseph Conway was your grandfather...did he go by "Con"? If so, what is your father's name? My husband's grandfather is Elbert Simpson Burnette, Jr. His father, Elbert Simpson, Sr., "Eb", had a 3 brothers: One called "Con", short for Conway, but we aren't sure of a second name, another called "Ben" short for Bennett, and the third called "Jar", but we're unsure of his real name. Their father was named David Jackson Burnette and went by Jack, but as far as we know...they all lived in or around the Columbus, NC area at one time. I am eager to hear back from you to see if we can fill any gaps of our history knowledge.
I hope you are having a wonderful holiday season!